From Clouatre-Ostermann-Ransford to Okubo-Ando

Abstract

We prove that if $θ$ is a continuous unital homomorphism of an operator algebra $A$ into $B(\mathcal{H})$, and $β$ is in the dual space of $A$, then the completely bounded norm of $θ$ is less than or equal to the maximum of $1$ and the completely bounded norm of $θ+ βI $. As an application, we give another proof of the Okubo--Ando theorem.